Anomalous length dependence of the conductance of graphene nanoribbons with zigzag edges.

Charge transport through two sets of symmetric graphene nanoribbons with zigzag shaped edges in a two-terminal device has been investigated, using density functional theory combined with the non-equilibrium Green's function method. The conductance has been explored as a function of nanoribbon length, bias voltage, and the strength of terminal coupling. The set of narrower nanoribbons, in the form of thiolated linear acenes, shows an anomalous length dependence of the conductance, which at first exhibits a drop and a minimum, followed by an evident rise. The length trend is shown to arise because of a gradual transformation in the transport mechanism, which changes from being governed by a continuum of out-of-plane π type and in-plane state channels to being fully controlled by a single, increasingly more resonant, occupied π state channel. For the set of nanoribbons with a wider profile, a steady increase is observed across the whole length range, owing to the absence of the former transport mechanism. The predicted trends are confirmed by the inclusion of self-interaction correction in the calculations. For both sets of nanoribbons the replacement of the strongly coupling thiol groups by weakly bonding phenathroline has been found to cause a strong attenuation with the length and a generally low conductance.